Topography prediction using system state information

ABSTRACT

Embodiments presented herein provide techniques for predicting the topography of a product produced from a manufacturing process. One embodiment includes generating a plurality of prediction models. Each of the plurality of prediction models corresponds to a respective one of a plurality of positional coordinates of a product produced from a manufacturing process. The method also includes receiving a set of user-specified input parameters to apply to the manufacturing control process. The method further includes generating a graphical representation of a topography map for the product for the user-specified of input parameters based on the plurality of prediction models.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims benefit of U.S. Provisional Patent ApplicationSer. No. 62/203,229, filed on Aug. 10, 2015, and titled “TOPOGRAPHYPREDICTION USING SYSTEM STATE INFORMATION,” which is incorporated byreference herein in its entirety.

BACKGROUND

Field

Embodiments of the present disclosure generally relate to manufacturingprocesses, and more particularly to techniques for predicting thetopography of a product produced from a manufacturing process.

Description of the Related Art

In many manufacturing industries, the geometry of devices continues todecrease in size since such devices were first introduced severaldecades ago. In semiconductor manufacturing, for example, integratedcircuits have generally followed “Moore's Law,” which states that anumber of devices fitting on a chip will double every two years. As thedemand for higher yield devices is expected to increase further yet, theneed to achieve high-yield, high quality devices has prompted issues notpreviously considered to emerge as areas of concern. One such issuerelates to the topography of a product produced from a manufacturingprocess.

Generally, in manufacturing, the topography of a product that resultsfrom production is often a key factor that relates to the quality and/oryield of the product. For example, in semiconductor manufacturing, manyprocesses (e.g., such as deposition, etching, oxidation, etc.) used inthe fabrication of semiconductor devices can result in changes in theshape and/or composition of a wafer surface. Such changes, in turn, canresult in significant differences in yield of the product (e.g., thenumber of good die on the wafer), final feature quality of the product(e.g., aspect ratio or some other quality associated with features, suchas trenches, contact holes, vias, etc.), and/or performance of theproduct (e.g., insulating properties, etc.). As such, improved controlover the resulting topography of a product produced from a manufacturingprocess is necessary to ensure that the final product does not have lowyield, low quality, and/or low performance.

Currently in manufacturing, topography and its impact is typicallyassessed post-process. For example, conventional techniques typicallyrely on yield management systems, post-process, to detect potentialyield issues with a resulting product (e.g., detecting whether apercentage yield loss is present in the product). Once the issues areidentified, the conventional techniques rely on data mining to identifythe processes and/or process settings that should be adjusted. Assessingtopography, however, in this manner is extremely inefficient andtime-consuming. For example, closing the loop (e.g., finding the optimalprocess settings, processes, etc.) can often take weeks, during whichsignificant quality reduction and/or yield loss can occur until theproblem is identified, appropriate corrective action is determined, andthe corrective action is implemented.

In addition, other conventional techniques that attempt to address theabove issues typically perform post-process metrology data monitoringand mining to identify topographical anomalies and relate the identifiedanomalies to processing issues in the manufacturing process. Thesetechniques, however, are also inefficient at correcting any identifiedproblems, as these techniques are post-process techniques and as such donot prevent the current product (e.g., wafer lot, etc.) from having lowyield, quality, or performance. For example, with these techniques, oncetopographical anomalies are identified, the techniques typically rely onmanual (or human guided) methods to correct parameters of the currentprocess (and possibly upstream processes) to reduce the problem forfuture wafers. However, performing a correction process in this mannerleads to inexact results (e.g., due to human error), is not alwaysimmediate, and is incapable of improving yield of the current product orproduct lot.

SUMMARY

Embodiments disclosed herein include methods, systems, and computerprogram products for predicting the topography of a product producedfrom a manufacturing process. In one embodiment, a method for predictingthe topography of a product produced from a manufacturing process isdisclosed. The method includes generating a plurality of predictionmodels. Each of the plurality of prediction models corresponds to arespective one of a plurality of positional coordinates of a productproduced from a manufacturing process. For example, generating theplurality of prediction models includes, for each of the plurality ofprediction models, measuring, for each of a plurality of sets of inputparameters, by operation of one or more sensor devices, for each of aplurality of sets of input parameters, a sensor value at thecorresponding positional coordinate, during a respective iteration ofthe manufacturing process that is configured using the set of inputparameters. A respective prediction model is then generated, based onthe plurality of measured sensor values. The method also includesgenerating a graphical representation of a topography map for theproduct for a user-specified set of input parameters. For example,generating the graphical representation includes determining, for eachof the plurality of prediction models, a respective predicted value forthe corresponding positional coordinate of the product, and generating,using an interpolation function, a predicted value for at least oneother positional coordinate of the product not included in the pluralityof positional coordinates.

Another embodiment provides a non-transitory computer-readable mediumcontaining computer program code that, when executed, performs anoperation. The operation includes generating a plurality of predictionmodels. Each of the plurality of prediction models corresponds to arespective one of a plurality of positional coordinates of a productproduced from a manufacturing process. For example, generating theplurality of prediction models includes, for each of the plurality ofprediction models, measuring, for each of a plurality of sets of inputparameters, by operation of one or more sensor devices, for each of aplurality of sets of input parameters, a sensor value at thecorresponding positional coordinate, during a respective iteration ofthe manufacturing process that is configured using the set of inputparameters. A respective prediction model is then generated, based onthe plurality of measured sensor values. The operation also includesgenerating a graphical representation of a topography map for theproduct for a user-specified set of input parameters. For example,generating the graphical representation includes determining, for eachof the plurality of prediction models, a respective predicted value forthe corresponding positional coordinate of the product, and generating,using an interpolation function, a predicted value for at least oneother positional coordinate of the product not included in the pluralityof positional coordinates.

Still another embodiment provides a manufacturing system. Themanufacturing system includes a plurality of tools for manufacturing oneor more semiconductor devices, at least one processor, and a memory. Thememory stores a computer program that, when executed by the at least oneprocessor, performs an operation. The operation includes generating aplurality of prediction models. Each of the plurality of predictionmodels corresponds to a respective one of a plurality of positionalcoordinates of a semiconductor wafer produced from a manufacturingprocess. For example, generating the plurality of prediction modelsincludes, for each of the plurality of prediction models, measuring, foreach of a plurality of sets of input parameters, by operation of one ormore sensor devices, for each of a plurality of sets of inputparameters, a sensor value at the corresponding positional coordinate,during a respective iteration of the manufacturing process that isconfigured using the set of input parameters. A respective predictionmodel is then generated, based on the plurality of measured sensorvalues. The operation also includes generating a graphicalrepresentation of a topography map for the semiconductor wafer for auser-specified set of input parameters. For example, generating thegraphical representation includes determining, for each of the pluralityof prediction models, a respective predicted value for the correspondingpositional coordinate of the semiconductor wafer, and generating, usingan interpolation function, a predicted value for at least one otherpositional coordinate of the semiconductor wafer not included in theplurality of positional coordinates.

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentdisclosure can be understood in detail, a more particular description ofthe disclosure, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this disclosure and are therefore not to beconsidered limiting of its scope, for the disclosure may admit to otherequally effective embodiments.

FIG. 1 illustrates a block diagram of an example architecture of amanufacturing system that includes a topography prediction component, inaccordance with embodiments of the present disclosure.

FIG. 2 illustrates a block diagram of a topography prediction componentdetermining a topography map, in accordance with embodiments of thepresent disclosure.

FIG. 3 illustrates an example user interface for showing a predictedtopography map for a set of user-specified input parameters, inaccordance with embodiments of the present disclosure.

FIG. 4 is a flow diagram illustrating a method for predicting thetopography of a product produced from a manufacturing process, inaccordance with embodiments of the present disclosure.

FIG. 5 is a flow diagram illustrating a method for generating aplurality of prediction models, in accordance with embodiments of thepresent disclosure.

FIG. 6 is a flow diagram illustrating a method for generating agraphical representation of a topography map for a product produced froma manufacturing process, in accordance with embodiments of the presentdisclosure.

FIG. 7 is a flow diagram illustrating a method for determining anoptimized set of input parameters to apply to a manufacturing process,in accordance with embodiments of the present disclosure.

FIGS. 8A-8B illustrate example user interfaces for showing a determinedoptimized set of input parameters, in accordance with embodiments of thepresent disclosure.

FIG. 9 illustrates an example of a computing system configured with atopography prediction component, in accordance with embodiments of thepresent disclosure.

To facilitate understanding, identical reference numerals have beenused, wherever possible, to designate identical elements that are commonto the Figures. Additionally, it is contemplated that elements disclosedin one embodiment may be beneficially used in other embodimentsdescribed herein without specific recitation.

DETAILED DESCRIPTION

Embodiments presented herein present methods, computer-program products,and systems for predicting the topography (e.g., surface shape and/orcomposition) of a product produced from a manufacturing process. As willbe described in more detail below, embodiments presented providetechniques to predict the potential occurrence of quality and/or yieldissues (e.g., resulting from a set of input parameters, etc.) for aproduct, techniques to investigate the problem along with any potentialsolutions, and techniques to automatically provide an optimized solutionto reduce (or prevent) the occurrence of quality and/or yield issues forthe product. As also described in more detail below, the techniquespresented herein can be used to determine one or more optimizedparameter settings (e.g., to apply to a manufacturing process) given aset of input and output constraints (e.g., maximum and minimum thresholdvalues, granularity of adjustment capability, weighting indicating inputparameter adjustment preference, etc.) and objectives. As such, theembodiments presented herein allow manufacturing systems tosubstantially reduce (e.g., compared to traditional techniques) theoccurrence of quality and/or yield degradation of a product that canresult due to topographical issues.

One embodiment includes a method for predicting a topography map of aproduct produced from a manufacturing process. The method includesgenerating (by a topography prediction (TP) component) a plurality ofprediction models, where each of the plurality of prediction modelscorresponds to a respective one of a plurality of positional coordinatesof a product produced from a manufacturing process. For example, todetermine each respective prediction model, the TP component measures(e.g., by operation of one or more sensor devices), for each of aplurality of sets of input parameters, a sensor value at the respectivepositional coordinate during a respective iteration of the manufacturingprocess that is configured using the respective set of input parameters.The TP component then generates, for each respective positionalcoordinate, a prediction model based on the plurality of measured sensorvalues.

The TP component further generates a graphical representation of atopography map for the product for a user-specified set of inputparameters. For example, the TP component determines, for each of theplurality of prediction models, a respective predicted value for therespective positional coordinate of the product. The TP component thengenerates, using an interpolation function, a predicted value for atleast one other positional coordinate of the product not included in theplurality of positional coordinates. The topography map for the userspecified set of input parameters is then generated from the determinedpredicted values and the generated predicted values. Doing so in thismanner allows manufacturing systems to quickly identify and solve anypotential topographical issues that could affect the quality and/oryield of a product.

Note that, in the following description, many of the followingembodiments use semiconductor wafer processing as a reference example ofa manufacturing process where the techniques for topography predictiondescribed herein can be used to significantly improve (compared totraditional methods) the quality and/or yield of semiconductor wafers.Note, however, that the techniques presented herein can also be appliedin other industries, to other manufacturing processes, or, in general,any area where topography or an aspect of topography is altered by aprocess and the topography impacts the quality or yield of a desiredoutput. For example, applications could include semiconductor waferprocessing, display panel processing, a variety of different machiningprocesses, solar processing, etc. Further, in some cases, the techniquescould also be implemented outside of production (e.g., applied toanalysis, design, etc. in a variety of different fields).

FIG. 1 is a block diagram illustrating an architecture 100, in whichaspects of the present disclosure may be practiced. For example, in oneembodiment, the architecture 100 is an example of a manufacturing system(or environment), such as a semiconductor manufacturing system. Asdescribed below, in one embodiment, the techniques presented hereinallow the manufacturing system to predict the topography of a product(such as a semiconductor wafer, etc.) given a user-specified set ofinput parameters (e.g., a recipe setting that is to be applied to asemiconductor manufacturing process, etc.). Alternatively, oradditionally, embodiments also allow the manufacturing system todetermine an optimal set of input parameters (such as an optimizedrecipe setting) to apply to a manufacturing process, given a set ofmultiple input and output constraints and objectives. The objectives, ingeneral, can be any set of objectives with a goal that minimizes ormaximizes one or more physical properties of the product.

As shown, the architecture 100 includes a manufacturing control system(MCS) 102, process system 110 and a prediction system 118 connected viaa network 126. In general, the network 126 can be a wide area network(WAN), local area network (LAN), wireless LAN (WLAN), etc. The MCS 102and prediction system 118 can be any kind of physical computing systemhaving a network interface, such as a desktop computer, laptop computer,mobile device, tablet computer, server computing systems, and the like.

Process system 110 includes components 112 and sensors 114. Thecomponents 112, in some embodiments, can represent tools, equipments,systems, chambers, pumps, etc., that are used for one or moremanufacturing processes (e.g., semiconductor processing, solarprocessing, flat panel processing, LED processing, etc.) within processsystem 110. In the case of semiconductor manufacturing, for example,components 112 can include an etch chamber, a chemical vapor deposition(CVD) chamber, a physical vapor deposition (PVD) chamber, an atomiclayer deposition (ALD) chamber, an implant chamber, an annealingchamber, a plasma treatment chamber, or other processing chamber, eitheralone or in combination with one or more other chambers. In one example,process system 110 can produce one or more semiconductor wafers and canuse a manufacturing process, such as a PVD process, CVD process, ALDprocess, etc., to deposit one or more films on the semiconductor wafers.

Sensors 114 are generally configured to measure one or more attributesof a product produced within the process system 110. For example,sensors 114 can include metrology equipment used for measuring anattribute of a substrate (such as sheet resistance, temperature,thickness, etc.) of a substrate (e.g., a semiconductor wafer) producedwithin process system 110. In some embodiments, the metrology equipmentmay measure critical dimensions across the substrate and alter processparameters to change processing, by components 112, of the substrate. Insome embodiments, sensors 114 may be incorporated within one or morecomponents 112. In other embodiments, sensors 114 may be locatedexternal to one or more components 112, or other convenient location.

The MCS 102 is generally configured to control, via process controller106, components 112 within process system 110. Process controller 106,in general, can control all aspects of operation of the process system110 via direct control of components 112 and sensors 114 within processsystem 110, and/or via one or more other controllers (not shown) coupledto components 112 within process system 110. In one embodiment, theprocess controller 106 can control the process recipes in one or more ofthe components 112. For example, the process controller 106 may controlvacuum, chamber temperature, radio frequency (RF), power, gas flow rate,capacitance, spacing (e.g., between a wafer and target), and variousother processing parameters of the process recipe. In embodiments, theprocess controller 106 uses feedback from sensors 114 to monitor asubstrate undergoing processing in the process system 110, anddetermines based, in part, on the feedback whether to alter the processrecipe.

As shown, the MCS 102 also includes a plurality of process controlapplications 108 for interacting with the process controller 106 tocontrol operation of process system 110. In general, the MCS 102 cansupport a variety of process control applications 108 used for advanceprocess control (APC) and/or management of components 112 in processsystem 110. Examples of various applications related to APC that can beimplemented by MCS 102 include, but are not limited to, applications forfault detection (FD), run-to-run (R2R) control, equipment performancetracking (EPT) (e.g., of components 112), statistical process control(SPC), etc.

The MCS 102 also includes a user interface 104 (e.g., a graphical userinterface (GUI)) that allows a user to interact with any of thecomponents within the architecture 100. For example, as described below,using the user interface 104, a user can select one or more specificcomponents 112 to perform processing, apply one or more user-definedprocess parameters (e.g., one or more process recipes, etc.), receiveinput and output information (e.g., property and performance statisticsregarding a resulting product produced in the process system 110),topography map information, etc. Additionally, as described below, thetechniques presented herein also allow a user (via the user interface104) to adjust process parameters and determine (in real-time) theimpact of adjusting the process parameters on the topography of aproduct. For example, as a user continually adjusts one or more inputsfor a manufacturing process (e.g., for semiconductor wafers),embodiments can determine in real-time predicted topography maps for asemiconductor wafer corresponding to the different inputs. Further,embodiments allow a user (via the user interface 104) to determine anoptimized set of process parameters for a given set of input and outputconstraints and a list of objectives (e.g., for the topography) for theproduct. As such, the user interface 104 (with the techniques presentedherein) provides an improved investigation tool, compared to traditionaltools, for investigating potential issues with a product and determiningan optimal set of inputs (process parameters) to achieve a particulartopography.

Advanced manufacturing systems typically support various differentpredictive applications to improve the control of their systems. Some ofthese applications include applications for predictive maintenance,yield prediction, virtual metrology, and the like. These predictiveapplications, however, are insufficient for efficiently determining theimpact of topography on the quality and/or yield of a product producedfrom a manufacturing process. For example, as mentioned above, for manyof these techniques, identifying topography and its impact on aparticular product takes a significant period of time (e.g., weeks insome cases). Further, many of these techniques typically do not assesstopography and its impact across the entire product. For example, inthese techniques, typically only a portion (such as the middle orcenter) of the product is assessed to determine topography at theportion, while other portions (such as edges of the product) are notconsidered. As the drive to increase yield and quality of devicescontinues to increase, however, it is becoming increasingly moreimportant to consider topography at edges of the product, for example,to determine whether uniformity exists across the entire surface of aproduct.

Accordingly, as shown, the prediction system 118 includes a topographyprediction (TP) component 120, which allows the MCS 102 to efficientlydetermine the topography of a product produced within process system 110and its impact on the quality and/or yield of the product. The TPcomponent 120 generally represents logic (e.g., a software application,device firmware, an ASIC, etc.) that is configured to implement one ormore of the techniques presented herein. For example, the TP component120 could perform method 400 illustrated in FIG. 4, method 500illustrated in FIG. 5, method 600 illustrated in FIG. 6 and/or method700 illustrated in FIG. 7.

The TP component 120 includes a modeling engine 122 and a predictionengine 124. As described in more detail below (e.g., in FIGS. 2, and4-7), the modeling engine 122 is configured to generate (e.g., based onsensor data) a plurality of prediction models (or positional coordinatemodels) for a product produced within process system 110, where each ofthe plurality of prediction models corresponds to a respective one of aplurality of positional coordinates of the product. Doing so in thismanner allows the TP component 120 to determine topography across theentire surface of a product (as opposed to only determining, withconventional techniques, topography at the center of a product).

Further, as also described in more detail below (e.g., in FIGS. 2 and4-7), the prediction engine 124 is configured to determine, for each ofthe plurality of prediction models, a respective predicted value for therespective positional coordinate of the product. In one embodiment, thepredicted value corresponds to a predicted measurement value ofparticular physical property (e.g., thickness, resistivity, temperature,surface roughness, etc.) of the product at the respective positionalcoordinate. The prediction engine is also configured to generate, usingan interpolation function, a predicted value for at least one otherpositional coordinate of the product not included in the plurality ofpositional coordinates.

The prediction engine 124 then generates a graphical representation of atopography map for the product for a user-specified set of inputparameters based, at least in part, on the determined predicted valuesand the generated predicted values. Such topography map can be displayedto a user via the user interface 104. The user can then interactivelyadjust, via the user interface 104, one or more input parameters toinvestigate, in real-time, the impact on the topography of the product.Doing so allows a user to proactively determine the impact differentvalues for input parameters of a manufacturing process (e.g.,semiconductor manufacturing process) may have on the topography of aproduct produced from the manufacturing process (e.g., semiconductorwafer), as opposed to conventional techniques which typically assess thetopography impact post-process.

In the depicted embodiment, the prediction system 118 is coupled tostorage system 116 and can use storage system 116 to store data receivedfrom sensors 114A-N, prediction models produced by modeling engine 122,positional coordinates for a product produced by the process system 110,predicted values, generated topography maps, and other information. Inone embodiment, the storage system 116 represents an example of adatabase, such as an Oracle® database. In other embodiments, the storagesystem could be a storage system that uses an Apache™ Hadoop® basedtechnology, such as a Hadoop Distributed Filing System (HDFS). Ofcourse, one of ordinary skill in the art will recognize that suchexamples are provided for illustrative purposes only, and moregenerally, embodiments may be configured to use any type of storagesystem, or combination of storage systems.

Note, however, that FIG. 1 illustrates merely one possible arrangementof the architecture 100. More generally, one of ordinary skill in theart will recognize that other embodiments of manufacturing systems canalso be configured to implement topography prediction in accordance withthe techniques presented herein. For example, although MCS 102 andprediction system 118 are shown as separate entities, in otherembodiments, the MCS 102 and prediction system 118 can be included as apart of one computing system. Further, although the illustratedprediction system 118 includes only the TP component 120, the predictionsystem 118 could also include other predictive applications, such asthose used for predictive maintenance, virtual metrology, and the like.

FIG. 2 illustrates an example scenario 200 of the TP component 120determining a topography map, according to one embodiment. To generate aplurality of prediction models, the TP component 120 first performs, foreach of a plurality of sets of input parameters (e.g., parameter set 1,parameter set 2, . . . , parameter set M), an iteration of themanufacturing process (e.g., iteration 1, iteration 2, . . . , oriteration N) that is configured using the respective set of inputparameters. In general, each iteration of the manufacturing process maybe performed for a different wafer (e.g., one of wafers 202A-N). These Nwafers typically correspond to one design of experiment (DOE) used todetermine relationships between various inputs and outputs. The number Nof iterations can depend on one or more various criteria, such as themanufacturing process complexity, tool complexity, etc. In oneembodiment, the number N of iterations corresponds to the number ofparameters in a particular parameter set (e.g., five iterations if thereare five parameters in parameter set 1).

During each iteration, the TP component 120 measures, by operation ofsensors 114, a sensor value at each positional coordinate 204 for therespective wafer 202. At each positional coordinate 204 of a givenwafer, the TP component 120 may receive a measured sensor value for eachsensor 114, where each sensor value corresponds to a measurement of aphysical property of the respective wafer. For example, in oneembodiment, if there are two sensors 114 (one for measuring thicknessand one for measuring temperature), the TP component 120 would receivetwo measured sensor values (e.g., for thickness and temperature) at eachpositional coordinate 204 of a given wafer.

In one embodiment, after the TP component 120 completes the measurementprocess for the current iteration, the TP component 120 varies one ormore parameter values in the next parameter set (e.g., parameter set 2)from their respective values in the previous parameter set (e.g.,parameter set 1). The TP component 120 then performs the measurementprocess for the second wafer (e.g., wafer 202B). In general, thisprocess continues until the TP component 120 measures a sensor value ateach respective positional coordinate 204 (of wafer N) during aniteration N of the manufacturing process that is configured usingparameter set N. Doing so in this manner provides the TP component 120with a set of historical data that the TP component 120 can use todevelop prediction models. Each of these prediction models relatessystem states to one or more values relating to the topography (e.g.,thickness) at the respective positional coordinate. Note that althoughFIG. 2 illustrates one particular pattern of two-dimensional(x_(i),y_(i)) positional coordinates on a wafer, in general, anyarrangement (random or not) of (x_(i),y_(i)) positional coordinates canbe used for the wafers.

As shown, once the TP component 120 completes all iterations, modelingengine 122 of the TP component 120 uses the measured sensor values 220to generate a plurality of prediction models 206, one prediction modelfor each positional coordinate. In one embodiment, the TP component 120maps (or fits) a function (e.g., using a least squares analysis, robustlinear fit, ridge regression, or other regression technique, etc.) tothe plurality of measured sensor values and uses the mapped function tobuild a prediction model for each positional coordinate. In one example,the function is based on a characteristic of the plurality of measuredsensor values. For example, depending on the dataset, the TP component120 may map a linear or non-linear function to the measured sensorvalues. In one embodiment, the TP component 120 builds a predictionmodel 206 for each measured sensor value at each positional coordinate.For example, if there are forty-nine positional coordinates and twomeasured sensor values for thickness and temperature at each positionalcoordinate, the TP component would build ninety-eight prediction models(e.g., forty-nine for predicting thickness of the wafer, and forty-ninefor predicting temperature of the wafer).

Once the TP component 120 generates the plurality of prediction models206, the prediction models 206 can be stored (e.g., in storage system116) until needed by the prediction engine 124. For example, as shown,once the prediction engine 124 receives a user-specified set of inputparameters 208, the prediction engine generates a predicted topographymap for the product for the user-specified set of input parameters 208.To generate the topography map, the prediction engine 124 determines,for each of the plurality of prediction models 206, a respectivepredicted value for each respective positional coordinate of theproduct. The prediction engine 124 then interpolates, using one of theinterpolation techniques 210, between the positional coordinates todetermine a predicted value for any positional coordinates not includedin the plurality of positional coordinates. Such interpolationtechniques can be used between the positional coordinates to smooth thepredicted values between neighboring positional coordinates and increasethe prediction quality.

The prediction engine 124 can select any of several interpolationtechniques 210 to perform interpolation. Examples of such interpolationtechniques 210 include, but are not limited to, inverse distanceweighting (IDW) interpolation, Kriging interpolation, Natural Neighborinterpolation, Spline interpolation, and the like. In one embodiment,the prediction engine 124 selects an interpolation technique based onthe physical property of the output. For example, in one embodiment, ifthe prediction engine 124 is predicting the temperature of the product,the prediction engine 124 selects Spline interpolation method to performinterpolation. In another embodiment, if the prediction engine 124 ispredicting thickness of the product, the prediction engine 124 selectsKriging interpolation method to perform interpolation. The predictionengine 124 then generates a graphical representation of the topographymap 212 based on the determined predicted values and the interpolatedpredicted values.

FIG. 3 illustrates an example graphical user interface (GUI) 300 for apredicted topography map, according to one embodiment. In oneembodiment, GUI 300 is an example of user interface 104 describedrelative to FIG. 1. As shown, GUI 300 includes a panel 302 and a panelwindow 306. Panel 302 includes a plurality of process parameters 304A-Ethat can be used to configure a manufacturing process of a product. Forexample, in this embodiment, panel 302 includes a process parameter 304Afor radio frequency (RF), process parameter 304B for power (DC), processparameter 304C for a gas flow rate, process parameter 304D for percentcapacitance, and a process parameter 304E for spacing (e.g., between awafer and target). Of course, one of ordinary skill in the art willrecognize that such examples are provided for illustrative purposesonly, and more generally, embodiments may be configured to use anynumber and/or any type of process parameters.

As shown, panel 306 includes a graphical representation of thetopography map 212. In one embodiment, the graphical representation ofthe topography map 212 is provided as a color coded two-dimensionalpicture to a user, via user interface 104, along with statistics such asmean, standard deviation, uniformity, topographical metrics, etc.,relating to predicted topography map 212. However, in general, thetopography map 212 can be graphically represented in other formats(e.g., shading, grayscale, etc.). As also shown, panel 302 includessliders for adjusting values of parameters 304A-E between theirrespective minimum and maximum values. In one embodiment, the wafertopography map 212 in panel 306 is automatically recomputed andre-visualized every time a parameter is changed via the sliders in panel302. Doing so in this manner allows a user to immediately determine theimpact, as a result of adjusting process parameters, on the topographyof a wafer. Note that the example GUI 300 illustrates one possiblepresentation of process parameters and a topography map. More generally,one of ordinary skill in the art will recognize that the GUI 300 mayinclude different configurations of the process parameters, differentconfigurations of the topography map, additional (or less) informationfields, etc.

FIG. 4 is a flow diagram of a method 400 for predicting the topographyof a product produced from a manufacturing process, according to oneembodiment. As shown, the method begins at block 402, where a TPcomponent 120 generates a plurality of prediction models. As describedabove, each of the plurality of prediction models corresponds to arespective one of a plurality of positional coordinates of a productproduced from a manufacturing process. At block 404, the TP component120 receives a user specified set of input parameters. In someembodiments, the user specified set of input parameters can include anyof process recipe settings, sensor and tool parameters, pre-processmetrology information (e.g., pre-process topography information),upstream process information (e.g., process parameters or post-processmetrology information), etc. At block 406, the TP component generates agraphical representation of a topography map for the product based, atleast in part, on the user specified set of input parameters and theplurality of prediction models.

FIG. 5 is a flow diagram of a method 500 for generating a plurality ofprediction models, according to one embodiment. As shown, the methodbegins at block 502, where a TP component 120 determines a plurality ofsets of input parameters. For example, as mentioned above, in oneembodiment, the TP component 120 determines the number of sets of inputparameters based on the processing complexity, tool complexity, etc. Atblock 502, the TP component 120 determines (e.g., based on processingcomplexity, tool complexity, desired model accuracy, etc.) a numberand/or location of positional coordinates of a product produced frommanufacturing process. For each input parameter set, the TP component120 then measures, by operation of one or more sensors, a sensor valueat a respective positional coordinate, during a respective iteration ofthe manufacturing process that is configured using the respective inputparameter set (block 506). In one embodiment, as noted above, beforeeach respective iteration of the manufacturing process, the TP component120 can vary, in the respective set of input parameters, at least oneparameter value from a parameter value in a previous respective set ofinput parameters before measuring the sensor value at each respectivepositional coordinate. At block 508, the TP component 120 thengenerates, for each positional coordinate, a respective predictionmodel, based on the plurality of measured sensor values.

FIG. 6 is a flow diagram of a method 600 for generating a topography mapfor a product produced from a manufacturing process, according to oneembodiment. As shown, the method begins at block 602, where a TPcomponent 120 determines (e.g., by performing method 500 or othertechniques described herein) a plurality of prediction models. At block604, the TP component 120 determines whether a set of user-specifiedinput parameters (e.g., process recipes, sensor and tool parameters,pre-process/post-process metrology information, etc.) has been received.If not, the TP component 120 remains at block 604. However, if the TPcomponent 120 determines that a set of input parameters has beenreceived, the TP component 120 determines, for each prediction model, arespective predicted value for a respective positional coordinate of theproduct (block 606). For example, as mentioned above, each predictedvalue corresponds to a predicted measurement of a physical property ofthe product (e.g., thickness, resistivity, temperature, surfaceroughness, etc.).

At block 608, the TP component 120 then generates, using aninterpolation function, a predicted value for at least one otherpositional coordinate of the product not included in the plurality ofpositional coordinates. At block 610, the TP component generates agraphical representation of a topography map for the product, based onthe determined predicted values and the generated predicted values. Asmentioned above, the graphical representation of the topography map canbe displayed to a user via a GUI, such as GUI 300.

At block 612, the TP component 120 determines whether there has been achange in at least one parameter value of the user-specified inputparameters. If so, the TP component determines an updated graphicalrepresentation of a topography map for the product based, at least inpart, on the changed parameter value and the plurality of predictionmodels (block 614). The TP component 120 then alters the generatedgraphical representation of the topography map to provide avisualization of the updated graphical representation (block 616),before returning to block 612. In one embodiment, the TP component 120determines for at least one continually adjustable input parameter ofthe user-specified input parameters, a plurality of updated graphicalrepresentations of the topography map for the product based in part onthe value of the adjustable input parameter and the plurality ofprediction models. The TP component 120 can continually alter thegenerated graphical representation of the topography map to providevisualizations of the updated graphical representations.

Doing so in this manner allows a user to determine, in real-time, anypotential impact of adjusting states, such as recipe inputs, on theproduct. For example, as mentioned above with reference to FIG. 3, auser can use sliders to adjust values of an input parameter between itsminimum and maximum values (e.g., corresponding to its actuationcapability). As the slider is moved, the TP component 120 cancontinually adjust the graphical representation in real-time to indicatethe impact of the changing input value, which allows the user toinvestigate and determine an optimal set of inputs to achieve aparticular topography (without having to rely on post-process methods todetermine impact to the topography).

As mentioned above, the techniques presented herein can also provide anoptimal set of input parameters to apply to a manufacturing processgiven a set of input and output constraints and list of objectives. FIG.7 is a flow diagram of a method 700 for determining an optimized set ofinput parameters to apply to a manufacturing process, according to oneembodiment. As shown, the method begins at block 702, where a TPcomponent 120 generates (e.g., using method 500 in FIG. 5 or othertechniques described herein) a plurality of prediction models. Asmentioned above, in some embodiments, the TP component generates aprediction model for each measured sensor value (measured physicalproperty of a product) at each positional coordinate.

At block 704, the TP component 120 determines whether a set of minimumand maximum thresholds for a set of user-specified input parameters hasbeen received. For example, in one embodiment, the set of minimum andmaximum thresholds (or constraints) could include at least one ofmaximum and minimum values corresponding to actuation capability of theprocess tools, granularity of adjustment capability, weightingindicating parameter adjustment preference, and the like. If the TPcomponent 120 determines that the set of input parameters has beenreceived, the TP component 120 determines whether a list of objectivesfor at least one physical property of a product produced from amanufacturing process has been received. In one embodiment, eachobjective in the list of objectives has a goal to minimize or maximize apredicted value for a plurality of positional coordinates of theproduct. For example, in one case, the TP component 120 could receive alist of two objectives, where the first objective's goal is to minimizethickness uniformity on the wafer and the second objective's goal is tomaximize (mean) resistivity on the wafer. In general, however, the TPcomponent 120 can receive any number and/or other list of objectives.

Further, in some embodiments, the TP component 120 could receive aweighting parameter for each objective. The weighting parameter, ingeneral, indicates to the TP component 120 whether the respectiveobjective should take precedence over another objective. For example,using the example above, in one embodiment, the TP component 120 canreceive a first weighting value for the objective to minimize thicknessuniformity and a second weighting value for the objective to maximizeresistivity, where the first weighting indicates to the TP component 120that the objective to minimize thickness uniformity should takeprecedence over the objective to maximize mean resistivity. As areference example, in one embodiment, if the first objective has aweighting value of ten and the second objective has a weighting value ofone, such weighting would indicate to the TP component 120 thatachieving the first objective is ten times as important as achieving thesecond objective.

If the TP component 120 determines that the list of objectives has beenreceived, the TP component 120 then determines an optimized set of inputparameters to apply to the manufacturing process based, at least inpart, on the plurality of prediction models, the received set ofthresholds, and the received list of objectives (block 708). Forexample, upon receiving the list of objectives, the TP component 120 canbuild a cost function subject to the constraints (e.g., thresholds andobjectives) and perform multi-objective optimization (e.g., usingtechniques such as linear programming, Monte Carlo simulation,evolutionary algorithms, or any multi-objective optimization algorithm)to find the optimal set of input parameters that satisfies all theconstraints (e.g., achieves each objective in the list of objectives, iswithin the set of thresholds, etc.).

Once the TP component 120 finds the optimal set of input parameters, theTP component 120 can display the optimal set of input parameters and thetopography maps for each obtained objective to a user (e.g., via userinterface 104). For example, as illustrated in GUI 800A of FIG. 8A, inone embodiment, the TP component 120 can display the optimized set ofinput parameters in a panel 802, and the topography map 806A showing theminimized thickness uniformity for the wafer in panel 804A.Additionally, as illustrated in GUI 800B of FIG. 8B, the TP component120 can display the topography map 806B showing the maximized meanresistivity for the wafer in panel 804B. In this embodiment, GUIs 800A-Balso include sliders for each of the optimized set of parameters toallow the user to adjust the parameters to determine in real-time theimpact to the topography maps 806A and 806B. Note, however, that theabove presentation of the optimized set of parameters in panel 802 andtopography maps 806A and 806B represent merely one example of aconfiguration that can be presented to a user. More generally, one ofordinary skill in the art will recognize that the GUIs 800A-B mayinclude different configurations of the process parameters, differentconfigurations of the topography maps, additional (or less) informationfields, etc.

FIG. 9 illustrates a computing system 900 configured to predict thetopography of a product produced from a manufacturing process, accordingto an embodiment. As shown the computing system 900 includes, withoutlimitation, a central processing unit (CPU) 905, a network interface915, a memory 920, and storage 930, each connected to a bus 917. Thecomputing system 900 may also include an I/O device interface 910connecting I/O devices 912 (e.g., keyboard, mouse, and display devices)to the computing system 900. Further, in context of this disclosure, thecomputing elements shown in the computing system 900 may correspond to aphysical computing system (e.g., a system in a data center) or may be avirtual computing instance executing within a computing cloud.

The CPU 905 retrieves and executes programming instructions stored inthe memory 920 as well as stores and retrieves application data residingin the memory 920. The interconnect 917 is used to transmit programminginstructions and application data between CPU 905, I/O devices interface910, storage 930, network interface 915, and memory 920. Note, CPU 905is included to be representative of a single CPU, multiple CPUs, asingle CPU having multiple processing cores, and the like. Memory 920 isgenerally included to be representative of a random access memory.Storage 930 may be a disk drive storage device. Although shown as asingle unit, storage 930 may be a combination of fixed and/or removablestorage devices, such as fixed disc drives, removable memory cards, oroptical storage, network attached storage (NAS), or a storagearea-network (SAN).

Illustratively, the memory 920 includes a TP component 922 and a userinterface 928. The TP component 922 includes a prediction engine 924 anda modeling engine 926. The storage 930 includes sensor data 932,positional coordinates 934 and prediction models 936. Further, althoughnot shown, memory 920 can also include a process controller (e.g.,process controller 106), one or more process control applications (e.g.,process control applications 108), one or more predictive applications,etc. In some embodiments, each of the sensor data 932, positionalcoordinates 934 and prediction models 936 may also be stored withinmemory 920.

In one embodiment, the TP component 922 generates (via modeling engine926) a plurality of prediction models for a plurality of coordinatepoints of a product to be produced by a manufacturing process. Once theTP component 922 receives a set of user-defined inputs (e.g., via userinterface 928), the TP component 922 (via prediction engine 924)generates a topography map for the product based, at least in part, onthe plurality of prediction models 936. The generated topography map isthen displayed to a user, via the user interface 928.

Alternatively, or additionally, in another embodiment, after generatingthe plurality of models, the TP component 922 receives a set of inputand output constraints for a set of parameters and a list of objectives.The TP component 922 then determines an optimal set of input parametersbased on the plurality of prediction models, input/output constraints,and list of objectives.

The descriptions of the various embodiments of the present disclosurehave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations will be apparent to those of ordinary skillin the art without departing from the scope and spirit of the describedembodiments. The terminology used herein was chosen to best explain theprinciples of the embodiments, the practical application or technicalimprovement over technologies found in the marketplace, or to enableothers of ordinary skill in the art to understand the embodimentsdisclosed herein.

As will be appreciated by one skilled in the art, aspects of the presentdisclosure may be embodied as a system, method or computer programproduct. Accordingly, aspects of the present disclosure may take theform of an entirely hardware embodiment, an entirely software embodiment(including firmware, resident software, micro-code, etc.) or anembodiment combining software and hardware aspects that may allgenerally be referred to herein as a “circuit,” “module” or “system.”Furthermore, aspects of the present disclosure may take the form of acomputer program product embodied in one or more computer readablemedium(s) having computer readable program code embodied thereon.

Any combination of one or more computer readable medium(s) may beutilized. The computer readable medium may be a computer readable signalmedium or a computer readable storage medium. A computer readablestorage medium may be, for example, but not limited to, an electronic,magnetic, optical, electromagnetic, infrared, or semiconductor system,apparatus, or device, or any suitable combination of the foregoing. Morespecific examples (a non-exhaustive list) of the computer readablestorage medium would include the following: an electrical connectionhaving one or more wires, a portable computer diskette, a hard disk, arandom access memory (RAM), a read-only memory (ROM), an erasableprogrammable read-only memory (EPROM or Flash memory), an optical fiber,a portable compact disc read-only memory (CD-ROM), an optical storagedevice, a magnetic storage device, or any suitable combination of theforegoing. In the context of this document, a computer readable storagemedium may be any tangible medium that can contain, or store a programfor use by or in connection with an instruction execution system,apparatus, or device.

A computer readable signal medium may include a propagated data signalwith computer readable program code embodied therein, for example, inbaseband or as part of a carrier wave. Such a propagated signal may takeany of a variety of forms, including, but not limited to,electro-magnetic, optical, or any suitable combination thereof. Acomputer readable signal medium may be any computer readable medium thatis not a computer readable storage medium and that can communicate,propagate, or transport a program for use by or in connection with aninstruction execution system, apparatus, or device.

Program code embodied on a computer readable medium may be transmittedusing any appropriate medium, including but not limited to wireless,wireline, optical fiber cable, RF, etc., or any suitable combination ofthe foregoing.

Computer program code for carrying out operations for aspects of thepresent disclosure may be written in any combination of one or moreprogramming languages, including an object oriented programming languagesuch as Java, C#, Smalltalk, C++ or the like and conventional proceduralprogramming languages, such as the “C” programming language or similarprogramming languages. The program code may execute entirely on theuser's computer, partly on the user's computer, as a stand-alonesoftware package, partly on the user's computer and partly on a remotecomputer or entirely on the remote computer or server. In the latterscenario, the remote computer may be connected to the user's computerthrough any type of network, including a local area network (LAN) or awide area network (WAN), or the connection may be made to an externalcomputer (for example, through the Internet using an Internet ServiceProvider).

Aspects of the present disclosure are described above with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems) and computer program products according to embodiments of thedisclosure. It will be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer program instructions. These computer program instructions maybe provided to a processor of a general purpose computer, specialpurpose computer, or other programmable data processing apparatus toproduce a machine, such that the instructions, which execute via theprocessor of the computer or other programmable data processingapparatus, create means for implementing the functions/acts specified inthe flowchart and/or block diagram block or blocks.

These computer program instructions may also be stored in a computerreadable medium that can direct a computer, other programmable dataprocessing apparatus, or other devices to function in a particularmanner, such that the instructions stored in the computer readablemedium produce an article of manufacture including instructions whichimplement the function/act specified in the flowchart and/or blockdiagram block or blocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present disclosure. In this regard, each block in theflowchart or block diagrams may represent a module, segment, or portionof instructions, which comprises one or more executable instructions forimplementing the specified logical function(s). In some alternativeimplementations, the functions noted in the block may occur out of theorder noted in the figures. For example, two blocks shown in successionmay, in fact, be executed substantially concurrently, or the blocks maysometimes be executed in the reverse order, depending upon thefunctionality involved. It will also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

While the foregoing is directed to embodiments of the presentdisclosure, other and further embodiments of the disclosure may bedevised without departing from the basic scope thereof, and the scopethereof is determined by the claims that follow.

What is claimed is:
 1. A method, comprising: generating a plurality ofprediction models, wherein each of the plurality of prediction modelscorresponds to a different one of a plurality of positional coordinatesof a product produced from a manufacturing process, and comprising, foreach of the plurality of prediction models: for each of a plurality ofsets of input parameters, performing a different iteration of themanufacturing process using the set of input parameters, and measuring,by operation of one or more sensor devices, a sensor value at thecorresponding positional coordinate, during the iteration of themanufacturing process that is configured using the set of inputparameters; and generating a prediction model for the correspondingpositional coordinate, based on the plurality of measured sensor values;and generating a graphical representation of a topography map for theproduct for a user-specified set of input parameters, comprising:determining, for each of the plurality of prediction models, a predictedvalue for the corresponding positional coordinate of the product; andgenerating, using an interpolation function, a predicted value for atleast one other positional coordinate of the product not included in theplurality of positional coordinates.
 2. The method of claim 1, furthercomprising, before each iteration of the manufacturing process: varying,in the respective set of input parameters, at least one parameter valuefrom a parameter value in a previous respective set of input parametersbefore measuring the sensor value at the corresponding positionalcoordinate.
 3. The method of claim 1, wherein generating the predictionmodel for the corresponding positional coordinate comprises: mapping afunction to the plurality of measured sensor values, wherein thefunction is based on a characteristic of the plurality of measuredsensor values; and using the mapped function to generate a predictionmodel for the different one of the plurality of positional coordinates.4. The method of claim 1, wherein the sensor value corresponds to ameasurement of at least one physical property of the product, andwherein the predicted value corresponds to a predicted measurement ofthe at least one physical property of the product.
 5. The method ofclaim 4, wherein using the interpolation function comprises: selectingthe interpolation function from a plurality of interpolation functions,based on the at least one physical property of the product, wherein theplurality of interpolation functions comprise at least one of an inversedistance weighting (IDW) function, a Kriging function, a naturalneighbor function, or a Spline function; and using the selectedinterpolation function to predict the measurement of the at least onephysical property of the product at the at least one other positionalcoordinate.
 6. The method of claim 5, wherein selecting theinterpolation function from the plurality of interpolation functionscomprises: selecting the Kriging function if thickness is the physicalproperty of the product; and selecting the Spline function iftemperature is the physical property of the product.
 7. The method ofclaim 1, further comprising: receiving a set of minimum and maximumthresholds for the input parameters; receiving a list of objectives forat least one physical property of the product, wherein each objective inthe list minimizes or maximizes the predicted values for the pluralityof positional coordinates of the product; and determining an optimizedset of input parameters to apply to the manufacturing process, based onthe plurality of prediction models, the received set of thresholds, andthe received list of objectives, wherein the optimized set of inputparameters achieves each objective in the list of objectives.
 8. Themethod of claim 7, wherein the at least one physical property for theproduct comprises at least one of thickness, resistivity, or surfaceroughness.
 9. The method of claim 1, further comprising: determining forat least one continually adjustable input parameter of theuser-specified set of input parameters, a plurality of updated graphicalrepresentations of the topography map for the product based in part on avalue of the adjustable input parameter and the plurality of predictionmodels; and continually altering the generated graphical representationof the topography map to provide visualizations of the updated graphicalrepresentations.
 10. The method of claim 1, wherein the productcomprises a semiconductor wafer, and wherein the manufacturing processcomprises a semiconductor manufacturing process used to deposit one ormore films on the semiconductor wafer.
 11. The method of claim 10,wherein the semiconductor manufacturing process used to deposit the oneor more films comprises one of a plasma vapor deposition (PVD) process,a chemical vapor deposition (CVD) process, or an atomic layer deposition(ALD) process.
 12. A non-transitory computer-readable medium containingcomputer program code that, when executed by a processor, performs anoperation comprising: generating a plurality of prediction models,wherein each of the plurality of prediction models corresponds to adifferent one of a plurality of positional coordinates of a productproduced from a manufacturing process, and comprising, for each of theplurality of prediction models: for each of a plurality of sets of inputparameters, performing a different iteration of the manufacturingprocess using the set of input parameters, and measuring, by operationof one or more sensor devices, a sensor value at the correspondingpositional coordinate, during the iteration of the manufacturing processthat is configured using the set of input parameters; and generating aprediction model for the corresponding positional coordinate, based onthe plurality of measured sensor values; and generating a graphicalrepresentation of a topography map for the product for a user-specifiedset of input parameters, comprising: determining, for each of theplurality of prediction models, a predicted value for the correspondingpositional coordinate of the product; and generating, using aninterpolation function, a predicted value for at least one otherpositional coordinate of the product not included in the plurality ofpositional coordinates.
 13. The non-transitory computer-readable mediumof claim 12, wherein the sensor value corresponds to a measurement of atleast one physical property of the product, and wherein the predictedvalue corresponds to a predicted measurement of the at least onephysical property of the product.
 14. The non-transitorycomputer-readable medium of claim 13, wherein using the interpolationfunction comprises: selecting the interpolation function from aplurality of interpolation functions, based on the at least one physicalproperty of the product, wherein the plurality of interpolationfunctions comprise at least one of an inverse distance weighting (IDW)function, a Kriging function, a natural neighbor function, or a Splinefunction; and using the selected interpolation function to predict themeasurement of the at least one physical property of the product at theat least one other positional coordinate.
 15. The non-transitorycomputer-readable medium of claim 14, wherein selecting theinterpolation function from the plurality of interpolation functionscomprises: selecting the Kriging function if thickness is the physicalproperty of the product; and selecting the Spline function iftemperature is the physical property of the product.
 16. Thenon-transitory computer-readable medium of claim 12, further comprising:receiving a set of minimum and maximum thresholds for the inputparameters; receiving a list of objectives for at least one physicalproperty of the product, wherein each objective in the list minimizes ormaximizes the predicted values for the plurality of positionalcoordinates of the product; and determining an optimized set of inputparameters to apply to the manufacturing process, based on the pluralityof prediction models, the received set of thresholds, and the receivedlist of objectives, wherein the optimized set of input parametersachieves each objective in the list of objectives.
 17. Thenon-transitory computer-readable medium of claim 12, further comprising:determining for at least one continually adjustable input parameter ofthe user-specified set of input parameters, a plurality of updatedgraphical representations of the topography map for the product based inpart on a value of the adjustable input parameter and the plurality ofprediction models; and continually altering the generated graphicalrepresentation of the topography map to provide visualizations of theupdated graphical representations.
 18. A manufacturing system,comprising: a plurality of tools for manufacturing one or moresemiconductor devices; at least one processor; and a memory containing aprogram that, when executed by the at least one processor, performs anoperation comprising: generating a plurality of prediction models,wherein each of the plurality of prediction models corresponds to adifferent one of a plurality of positional coordinates of asemiconductor wafer produced from a manufacturing process, andcomprising, for each of the plurality of prediction models: for each ofa plurality of sets of input parameters, performing a differentiteration of the manufacturing process using the set of inputparameters, and measuring, by operation of one or more sensor devices, asensor value at the corresponding positional coordinate, during theiteration of the manufacturing process that is configured using the setof input parameters, wherein the sensor value corresponds to ameasurement of at least one physical property of the semiconductorwafer; and generating a prediction model for the correspondingpositional coordinate, based on the plurality of measured sensor values;and generating a graphical representation of a topography map for thesemiconductor wafer for a user-specified set of input parameters,comprising: determining, for each of the plurality of prediction models,a predicted value for the corresponding positional coordinate of thesemiconductor wafer; and generating, using an interpolation function, apredicted value for at least one other positional coordinate of thesemiconductor wafer not included in the plurality of positionalcoordinates, wherein the predicted value corresponds to a predictedmeasurement of the at least one physical property of the semiconductorwafer.
 19. The manufacturing system of claim 18, wherein using theinterpolation function comprises: selecting the interpolation functionfrom a plurality of interpolation functions, based on the at least onephysical property of the semiconductor wafer, wherein the plurality ofinterpolation functions comprise at least one of an inverse distanceweighting (IDW) function, a Kriging function, a natural neighborfunction, or a Spline function; and using the selected interpolationfunction to predict the measurement of the at least one physicalproperty of the semiconductor wafer at the at least one other positionalcoordinate.
 20. The manufacturing system of claim 18, wherein theoperation further comprises: determining for at least one continuallyadjustable input parameter of the user-specified set of inputparameters, a plurality of updated graphical representations of thetopography map for the semiconductor wafer based in part on a value ofthe adjustable input parameter and the plurality of prediction models;and continually altering the generated graphical representation of thetopography map to provide visualizations of the updated graphicalrepresentations.